# Linear model selection (AIC/dredge function) with non parametric data (residuals are autocorrelated)

I used the dredge function with MuMIn & lme4 package to do a linear model selection with AIC principle. I have about 10 predictors (year, length of whale, 8 different fatty acid concentrations) to test for their effect on the dependent variable (Log transformed PCB concentration in whale blubber).

The best model is very interesting, there is no multicollinearity and the fitted residuals plot looks OK. HOWEVER, the Durbin-Watson test always fails (p < 0.05), meaning our residuals are autocorrelated... Does this invalidate my results and/or is this a problem? I am using model selection as it was advised by my supervisor, but the fatty acids I am including as predictors are proportional data (all adding to one) and tend to violate assumptions of normality and can be highly correlated. I had originally used a multivariate analysis (factor analysis) for my work, but was advised to use model selection to examine important predictors of sumPCB concentrations in whales (individual fatty acids, body size, and year). ... I tried a GLM model to correct for this autocorrelation but the results are different and less interesting, only one significant predictor...

Thank you for your feedback. As I am very new to these methods and approach (I am starting an MSc) I would appreciate any advice you have as I'm finding my dataset quite complicated for the model selection approach I was advised to do.

• Your model selection procedure invalidates your results. I'm not sure whether it's meaningful to determine if the DW result makes them 'more' invalid. The name of the function ("dredge") is an allusion to the fact that it is data dredging. It's worth reading the note in the documentation for the function. – gung - Reinstate Monica Jun 10 at 16:39
• 1) What are "parametric" and "nonparametric" data? // 2) Stepwise regression has been debunked on Cross Validated, and Gelman opposes stepwise regression. // 3) If you have many observations, tests are going to result in small p-values, even if the autocorrelation is not of practical significance. All the test is saying is, loosely speaking, there is not zero autocorrelation, but the autocorrelation could be $1/TREE(3)$ (unbelievably close to zero, yet not equal to zero). – Dave Jun 10 at 16:40
• @ReinstateMonica Well, my boss suggested the model selection in order to make sense of this huge multivariate dataset and find out more about which variables are more important in this beluga whale study. Other analyses will confirm this and be required of course. – Laura Zeppetelli-Bedard Jun 10 at 18:58
• You ask if it is a problem not to have parametric data, but what are parametric data? – Dave Jun 10 at 20:47